Determine if the system is time-invariant.

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Joined Jul 10, 2016
y[n] is a piece-wise function defining as below:
y[n] = x[n], n >=1
0, n = 0
x[n+1], n<=-1

So when applying time shift, x[n],0, and x[n+1] are time invariant by themselves but what about the bounds? If the understanding correctly, the bounds shift by n0 when y[n]--> y[n-n0] and we get n-n0>=1, n=n0, and n<=n0-1. Would they also shift if x[n]--->x[n-0]? Thanks!